Data Analysis using R

One-Way anova - Concept

Day10

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rm(list=ls())
rm(list=ls())
# oneway anova case I
#Data of three groups
water=c(10,12,18,24,36)
juice=c(11,14,19,23,38)
cof=c(12,13,17,25,37)

#Calculate the mean of the groups
mwater=mean(water)
mjuice=mean(juice)
mcof=mean(cof)
#Loading means into a vector
vm=c(mwater,mjuice,mcof)
vm

## [1] 20.0 21.0 20.8

#calculate sum of square within group 
ssw=sum((water-mwater)^2)
ssw

## [1] 440

ssj=sum((juice-mjuice)^2)
ssj

## [1] 446

ssc=sum((cof-mcof)^2)
ssc

## [1] 432.8

#Calculate mean sum of square within group
MSW=(ssw+ssj+ssc)/12
MSW

## [1] 109.9

#Calculate grand mean
gm=mean(vm)
gm

## [1] 20.6

#Calculate mean square between groups
MSB=sum(5*(vm-gm)^2)/2
MSB

## [1] 1.4

#F-Statitistics
F=MSB/MSW
F

## [1] 0.01273885

pf(MSB/MSW,2,12,lower.tail = FALSE)

## [1] 0.9873553

#P -value from F distribution
#Same example using R
grp=c(rep("g1",5),rep("g2",5),rep("g3",5))
grp

##  [1] "g1" "g1" "g1" "g1" "g1" "g2" "g2" "g2" "g2" "g2" "g3" "g3" "g3" "g3" "g3"

t=c(water,juice,cof)
t

##  [1] 10 12 18 24 36 11 14 19 23 38 12 13 17 25 37

df=data.frame(grp,t)
View(df)
#oneway anova from R Stat package
oneway.test(df$t~df$grp,,var.equal = TRUE)

## 
##  One-way analysis of means
## 
## data:  df$t and df$grp
## F = 0.012739, num df = 2, denom df = 12, p-value = 0.9874

# oneway anova case II
#Data of three groups
water=c(29,29,30,31,31)
juice=c(17,18,19,19,20)
cof=c(10,11,12,12,13)

#Calculate the mean of the groups
mwater=mean(water)
mjuice=mean(juice)
mcof=mean(cof)
#Loading means into a vector
vm=c(mwater,mjuice,mcof)
vm

## [1] 30.0 18.6 11.6

#calculate sum of square within group 
ssw=sum((water-mwater)^2)
ssw

## [1] 4

ssj=sum((juice-mjuice)^2)
ssj

## [1] 5.2

ssc=sum((cof-mcof)^2)
ssc

## [1] 5.2

#Calculate mean sum of square within group
MSW=(ssw+ssj+ssc)/12
MSW

## [1] 1.2

#Calculate grand mean
gm=mean(vm)
gm

## [1] 20.06667

#Calculate mean square between groups
MSB=sum(5*(vm-gm)^2)/2
MSB

## [1] 431.2667

#F-Statitistics
F=MSB/MSW
F

## [1] 359.3889

pf(MSB/MSW,2,12,lower.tail = FALSE)

## [1] 1.960539e-11

#P -value from F distribution
#Same example using R
grp=c(rep("g1",5),rep("g2",5),rep("g3",5))
grp

##  [1] "g1" "g1" "g1" "g1" "g1" "g2" "g2" "g2" "g2" "g2" "g3" "g3" "g3" "g3" "g3"

t=c(water,juice,cof)
t

##  [1] 29 29 30 31 31 17 18 19 19 20 10 11 12 12 13

df=data.frame(grp,t)
View(df)
#oneway anova from R Stat package
oneway.test(df$t~df$grp,,var.equal = TRUE)

## 
##  One-way analysis of means
## 
## data:  df$t and df$grp
## F = 359.39, num df = 2, denom df = 12, p-value = 1.961e-11